已知1999（x-y)+2000(y-z)-2001(x-y)=0

已知1999（x-y)+2000(y-z)+2001(x-z)=0
∴1999²(x-y)+2000²(y-z)+2001²(z-x)=2000,求z-y的值
1999（x-y)+2000(y-z)-2001(x-z)=0
1999x-1999y+2000y-2000z-2001x+2001z=0
-2x+y+z=0
∴x=(y+z)/2
1999²(x-y)+2000²(y-z)+2001²(z-x)=2000
1999²[(y+z)/2-y]+2000²(y-z)+2001²[(z-(y+z)/2]=2000
1999²(z-y)/2+2000²(y-z)+2001²(z-y)/2=2000
(z-y)(1999²-2*2000²+2001²)=2000
(z-y)[1999²-2*(1999+1)²+2001²]=2000
(z-y)(1999²-2*1999²-4*1999-2+2001²)=2000
(z-y)(2001²-1999²-4*1999-2)=2000
(z-y)(8000-7996-2)=2000
(z-y)*2=2000
∴z-y=1/1000

已知1999（x-y)+2000(y-z)+2001(x-z)=0
因为1999²(x-y)+2000²(y-z)+2001²(z-x)=2000，求z-y的值

1999（x-y)+2000(y-z)-2001(x-z)=0
1999x-1999y+2000y-2000z-2001x+2001z=0
-2x+y+z=0